Solution and Solid-State Behavior of Amphiphilic ABA Triblock Copolymers of Poly(acrylic acid-stat-styrene)-block-poly(butyl acrylate)-block-poly(acrylic acid-stat-styrene)

A combination of statistical and triblock copolymer properties is explored to produce stable aqueous polymer dispersions suitable for the film formation. In order to perform an extensive structural characterization of the products in the dissolved, dispersed, and solid states, a wide range of symmetrical poly(acrylic acid-stat-styrene)x-block-poly(butyl acrylate)y-block-poly(acrylic acid-stat-styrene)x, poly(AA-st-St)x-b-PBAy-b-poly(AA-st-St)x, (x = 56, 108 and 140, y = 100–750; the AA:St molar ratio is 42:58) triblock copolymers were synthesized by reversible addition–fragmentation chain transfer (RAFT) solution polymerization using a bifunctional symmetrical RAFT agent. It is demonstrated that the amphiphilic statistical outer blocks can provide sufficient stabilization to largely hydrophobic particles in aqueous dispersions. Such a molecular design provides an advantage over copolymers composed only of homoblocks, as a simple variation of the statistical block component ratio provides an efficient way to control the hydrophilicity of the stabilizer block, which ultimately affects the copolymer morphology in solutions and solid films. It was found by small-angle X-ray scattering (SAXS) that the copolymers behaved as dissolved chains in methylethylketone (MEK) but self-assembled in water into stable and well-defined spherical particles that increased in size with the length of the hydrophobic PBA block. These particles possessed an additional particulate surface structure formed by the statistical copolymer stabilizer block, which self-folded through the hydrophobic interactions between the styrene units. SAXS and atomic force microscopy showed that the copolymer films cast from the MEK solutions formed structures predicted by self-consistent field theory for symmetrical triblock copolymers, while the aqueous dispersions formed structural morphologies similar to a close-packed spheres, as would be expected for copolymer particles trapped kinetically due to the restricted movement of the blocks in the initial aqueous dispersion. A strong correlation between the structural morphology and mechanical properties of the films was observed. It was found that the properties of the solvent cast films were highly dependent on the ratios of the hard [poly(AA-st-St)] and soft (PBA) blocks, while the aqueous cast films did not show such a dependence. The continuous phase of hard blocks, always formed in the case of the aqueous cast films, produced films with a higher elastic modulus and a lower extension-to-break in a comparison with the solvent-cast films.


Characterisation of the synthesised triblock copolymers and their structural morphology in solutions/dispersions
Note: a These parameters were excluded from the model as the scattering pattern was truncated by the q-range limit of the SAXS measurements.

Characterisation of the triblock copolymer films
Structural characterization of triblock copolymer films cast from an organic solvent Solvent-cast films were drop-cast from a 40% w/w solution (approx. 100 µL) in MEK and formed transparent yellow films, where the yellowness of the film decreased as the triblock copolymer increased in molar mass. This reduction in yellow color is expected as the color is caused by the trithiocarbonate group present in the copolymers, the weight fraction of which decreases as the molar mass of the triblock copolymer increases. These films were cast onto dry-release film and left to dry under ambient conditions for 1 week. Where possible, the triblock film was removed from the silicone-coated dry-release film and transmission mode SAXS was performed on the free-standing film. Some triblock copolymer films were too soft and tacky to be removed without damage/distortion that may change their morphology. In these cases, SAXS was performed on the copolymer film whilst it was still attached to the dry-release film and a background scattering pattern of the dry-release film was subtracted from the combined scattering pattern.
It was expected that the hard and soft blocks within the triblock copolymer would undergo phase separation within the film and, since these two blocks have distinct scattering length densities, SAXS can be used to investigate the length scale of phase separation ( Figure S6). A peak in scattering intensity was observed in the majority of the SAXS patterns of the copolymer films cast from MEK. The presence of this peak indicates that there is a structural order, which is likely to be associated with copolymer block phase separation occurring within the films. 1 Figure S6. SAXS patterns of triblock copolymer films cast from a 40% w/w solution in MEK  increases. Scattering patterns were collected using a Xenocs Xeuss laboratory beamline.
Aside from the triblock copolymers with a short soft (B) block, the SAXS patterns of the solvent cast triblock copolymer films show a sharp peak in intensity suggesting that there is prominent phase separation within the films. The position of the primary peak (q*) indicates the length scale of the phase separation (d-spacing) which can be calculated using the equation . 1 The SAXS patterns for the individual triblock series (e.g., A108B100-750A108) shows that the primary peak position shifts to a lower q-value as the DP of the soft BA block is increased (Figures S6, and  Figure S7 and Table S3). Furthermore, increasing the overall triblock DP whilst maintaining a constant ratio of soft and hard units further increases the length of the phase separation (Table S3). Table S3. Structural analysis by SAXS and AFM investigating the bulk and surface phase separation of the solvent-cast copolymer films, respectively, where q* is position of the primary structural peak in the SAXS patterns, dSAXS is the real space distance corresponding to q* (dSAXS = 2/q*), and dAFM is the length scale of the phase separation measured by AFM ( Figure   S9). Structural morphology identified by AFM is given in the last column [Hex, BCC and Gyroid correspond to hexagonal-packed cylinders (space group P6/mm), body-centered cubic (space group Im3m) and gyroid cubic (space group Ia3d) structures, respectively]. The lattice period, a, was calculated using dSAXS-spacing assuming that the main peak corresponds to 100, 110 and 211 reflections of Hex, BCC and Gyroid structures, respectively.  Only one well-defined peak relating to the phase separated structure is observed in the SAXS patterns suggesting that the bulk structure of most of the compositions studied is not uniform.
Attempts to obtain a more ordered structure by annealing film above the hard block Tg at 150 °C overnight only led to a slight sharpening of the primary peak. Thus, the structural morphology of the copolymer film could not be assessed purely through peak position analysis of the SAXS patterns. AFM was used to further investigate the phase separation of the solvent cast triblock copolymer films ( Figure S8). Unlike transmission-mode SAXS which collects information from the entire bulk of the film, AFM is only able to assess the surface structure. To obtain a high-quality image the sample surface has to be flat. This was a problem for the films that had a high hard to soft block ratio, since the difference between the Young's moduli of the comprising copolymer blocks would distort the film upon drying resulting in a brittle, uneven film surface. Therefore, AFM images were not collected for A56B100A56, A108B100A108, A108B200A108, A140B100A140, A140B200A140 and A140B300A140. Some of these copolymer films demonstrated a weak or no phase separation in the SAXS patterns (e.g., A108B100A108, A140B100A140, and A140B200A140, Figure S6). The AFM height images of the triblock films cast from MEK ( Figure S8) indicate that there is phase separation visible on the surface of the films and that the structure and length of the phase separation varies with the copolymer composition. AFM images indicate that the length of the phase separation ( Figure S8) increases as the hard block DP and the soft block DP increases, which is consistent with the SAXS results (Table S3). Furthermore, copolymers with a similar same hard-to-soft block ratio but with an increasing total DP (e.g., A56B200A56, A108B300A108, and A140B500A140) show an increase in the length of the phase separation, which agrees with the SAXS results.
Unlike SAXS, the surface structures observed by AFM clearly show that the relative ratios of the hard and soft components within the triblock copolymer have a large effect on the phaseseparated structural morphology. Using the A108 triblock series as an example, A108B200A108 has fA of ~0.45 and possibly shows a biocontinuous structure ( Figure S8). However, as fA is    (Table S3) suggests that dSAXS are systematically smaller than dAFM. This apparent inconsistency is because the distances measured via SAXS are d-spacings corresponding to the crystallographic planes formed by objects structurally-ordered in three-dimensional space, whereas AFM measures distances between objects exposed to a two-dimensional surface which could correspond to a particular crystallographic plane. 1 Following the phase diagram of diblock copolymers 3 and AFM results ( Figure S8 and Table S3) Figure S11 and Table   S3). Figure S11. SAXS patterns of A108B750A108 and A108B500A108 triblock copolymer films cast from a 40% w/w solution in MEK (grey and pink symbols, respectively), where the arrows indicate the theoretical positions of the diffraction peaks for a BCC structure (grey arrows) and a hexagonal structure (pink arrows). The A108B750A108 pattern is shifted upwards (the multiplication factor is indicated on the plots) to avoid overlap. Scattering patterns were collected using a Xenocs Xeuss instrument.
For example, both a theoretical diblock copolymer phase diagram 3 and the AFM results ( Figure   S8) suggest that the scattering patterns of A108B750A108 and A108B500A108, demonstrating a similar q-value for the main peak position (Table S3) Figure   S11). Assuming that A108B750A108 has a BCC structure, the distance, d011, between the {011} crystallographic planes, measured from the main peak position of the A108B750A108 SAXS pattern, can be used to calculate the cubic lattice period, aBCC, according to: (S1) The shortest distance between nearest spheres forming a BCC structure could be calculated as a half of the cube diagonal length: Figure S12). Since d011 of A108B750A108 should be equal to 273 Å (Table S3), this converts into the BCC lattice period of aBCC = 386 Å and the shortest inter-particle distance of a = 334 Å. This calculated values representing distances between neighbouring particles in a BCC structure are reasonably consistent with the average distance between particles measured by AFM (dAFM = 353 Å, Table S3) and demonstrates the consistency between the two structural characterisation methods used within this paper. A similar calculation can be performed on copolymers that have a separation in the bulk represented by a hexagonally packed cylinders (e.g., A108B500A108). Inter-plane distances of a hexagonal structure relate to the lattice periods as: peak observed in the SAXS pattern should correspond to an inter-plane distance, d010, of 273 Å ( Figure S11). According to eq S2 this value converts to ahex = 315 Å corresponding to an inter-cylinder distance; again, this is similar to the distance measured by AFM (dAFM = 335 Å, Table S3).

Structural characterization of triblock copolymer films cast from aqueous dispersions
The films were prepared by drop-casting 20% w/w (approx. 100 µL) triblock copolymer dispersions onto dry release film in the same way to the films cast from MEK. Transmissionmode SAXS was used to investigate the size and structure of the phase separation within the bulk of the film and SAXS patterns were collected for all the triblock copolymer films ( Figure   S13).  The length scale of phase separation observed by SAXS for the films cast from water (Table   S4, Figure S13) shows a similar trend as for the films cast from MEK (Table S3 and Figure   S6), where the size of the phase separation increases as the length of either the soft or hard blocks, or the total triblock length, is increased. Despite these similarities between the aqueous cast films and the solvent cast films, the general structure of the phase separation is different as is demonstrated by the different shapes of the scattering patterns ( Figure S14). Generally, the water-cast triblock copolymer films show phase separation on a longer length scale. For example, the primary peak for each of the triblock copolymers appears at a lower q-value when cast from water rather than MEK (e.g., the peak for the A108B500A108 films appears at 0.0154 Å -1 in water and 0.0235 Å -1 in MEK). Furthermore, clear secondary and tertiary scattering intensity peaks are observed in some of the SAXS patterns of the water-cast films (e.g. peaks at approx. 0.03 and 0.04 Å -1 for A108B750A108, Figure S13b). The presence of these extra peaks suggests that the phase separation in the bulk of the film is better defined than in the solventcast films.
In addition to the high intensity peaks present at low q-values, there are a few peaks present in the high q region that are a result of smaller, well-ordered structures within the film. Similar to the solvent-cast films, the SAXS patterns of water-cast films contain a peak at q = 0.513 Å -1 that is likely to be a result of the PBA packing within the soft domains of the formed structures.
Another peak at q ~ 0.25 Å -1 , observed only for the water-cast films ( Figure S13), could be a result of the structure formed by packing of the statistical A block of a particulate nature proposed for the triblock copolymer particles ( Figure 5). The relative intensities of the two peaks vary with the copolymer composition, with the peak at q = 0.513 Å -1 increasing in intensity as the fraction of the soft block increases while the peak at q ~ 0.25 Å -1 becomes more prominent when the fraction of the hard block increases ( Figure S13). Thus, the relative intensities of these two peaks with respect to the copolymer composition further justify the cause of these structural peaks.
The SAXS patterns of the majority of the water-cast triblock copolymer films (A56B100-300A56, A108B100-300A108, and A140B100-300A140) were fit using a sphere form factor (equations S9-S12) combined with a structure factor of interacting hard spheres (eq S7) ( Figure S15). Comparison between the modelled spherical domain radius within the triblock copolymer films and the core radius of the particles in the aqueous dispersion showed that, generally, the domain size (Table   S4) is significantly smaller than the respective particle size (Table 3). This suggests that once the water has evaporated some of the PBA chains are no longer present in the well-defined core that is observed in the SAXS patterns and become part of the surrounding matrix ( Figure 9a).
However, this reduction in the domain size is not observed for the triblock copolymers with the largest hard (A) block length and a relatively small BA block (i.e., A140B100-200A140). This suggests the releasing of PBA chains from the core only occurs when the copolymer composition is weighted towards the soft block. Furthermore, it is only when the PBA block becomes larger (greater DP) than the total stabilizer block (A140B300A140) that a reduction in the domain size upon drying is observed. As the PBA core is highly hydrophobic, it is unlikely that the reduction in domain size is due to loss of water from the particle core. Additionally, the core domain size appears to be dominated largely by the size of the PBA block and is fairly independent of the length of the hard block. For example, A56B300A56, A108B300A108, and A140B300A140, have a hydrophobic domain size of 54 Å, 53 Å and 58 Å, respectively.

SAXS Structural Models
Intensity equation The intensity of the X-rays scattered by a particle dispersion, I(q), is expressed as: where ( , 1 , … , ) is the particle form factor defined by a k number of structural parameters, ( 1 , … , ) is a function describing dispersity of these parameters, ( ) is the structure factor describing particle interactions in the dispersion and N is the number density per unit sample volume defined as: where is the total particle volume fraction and ( 1 , … , ) is the particle volume.

Intensity equation with linear background
A plateau in intensity at high q was observed in the majority of the scattering patterns after subtraction of background scattering originating from the solvent and the sample holder (i.e., glass capillary). This scattering signal is likely to be associated with fluctuations in scattering length density across the particles caused by random distribution of monomer units in the selfassembled copolymers. In order to account for these fluctuations a linear fitting parameter (C1) that is independent of the scattering vector q was added to the equation describing the intensity of scattered X-rays (eq. S3): ( ) = ⋅ ( ) ⋅ ∫ . . . ∫ ( , 1 , . . . , ) ⋅ ( 1 , . . . , ) 1 . . .
Distribution function of the structural model parameters Only dispersity of particle radius, r, expressed as a Gaussian distribution, is considered for the structural models using eq. S3 (or equation S5): where R is the mean particle radius and σR is its standard deviation. All other fitting parameters describing the structural models where considered to be monodisperse (their distribution functions correspond to Dirac's delta function).
Hard sphere structure factor A hard sphere structure factor solved using the Percus-Yevick closure relation: 4 where RPY is an effective interparticle correlation radius and fPY is an effective volume fraction, has been incorporated into eq. S3 to account for long range interactions between the particles. 5 Form factor for a Gaussian chain A polymer molecule in theta solvent conditions behave as a Gaussian chain with a radius of gyration, Rg. In this case form factor of the polymer is described by a Debye function: Sphere model The self-assembled statistical copolymers studied in this work can be described as homogenous spherical particles. Thus, the form factor for eq. S3 (or equations S5) can be defined as: 6,7 ( , ) = agg ( ) 2 where r is the spherical particle radius, βs is the scattering length density (SLD) contrast of the particle defined as s = ( )( cop − sol ). Herein ( ) = Additionally, the molecule aggregation number can be calculated from the model parameters: where xsol is the volume fraction of solvent within the sphere and VA is the volume of a single copolymer molecule.

Two-population model
Generally, the intensity of the X-rays scattered by a particle dispersion, I(q), is defined by eq S3. However, in a case of core-shell spherical particles with a particulate shell ( Figure S15) eq. S3 should be altered to account for the additional surface structure: ( ) = 1 ( ) ⋅ 1 ⋅ ∫ 1 ( , 1 ) ⋅ ( 1 ) 1 + 2 ( ) ⋅ 2 ⋅ ∫ 2 ( , 2 ) ⋅ ( 2 ) 2 where the subscript 1 and 2 denotes the two populations of spherical particles, where the population 1 is assigned to the core-shell particles formed by triblock copolymers, and the population 2 to the particles comprising the triblock copolymer particle shell ( Figure S17).
Whereas the population 2 is described as a simple sphere and, therefore, 2 ( , 2 ) in eq S13 can be described using equations S9, S10, and S11 where it should be assumed that = 2 .
Additionally, the structure factors S1 and S2 are described using the hard-sphere structure factor solved using the Percus-Yevick closure relation (eq S7).

Gaussian distribution
The polydispersity of the particle radius, expressed as a Gaussian distribution, is considered for the structural model (eq S13): where R is the mean particle radius and σR is its standard deviation.